Stochastic stability analysis for the constant-modulus algorithm

We derive an easy-to-compute approximate bound for the range of step-sizes for which the constant-modulus algorithm (CMA) will remain stable if initialized close to a minimum of the CM cost function. Our model highlights the influence, of the signal constellation used in the transmission system: for smaller variation in the modulus of the transmitted symbols, the algorithm will be more robust, and the steady-state misadjustment will be smaller. The theoretical results are validated through several simulations, for long and short filters and channels.

SELF-SIMILARITY AND LAMPERTI CONVERGENCE FOR FAMILIES OF STOCHASTIC PROCESSES

We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to certain important families of processes that are not self-similar in the conventional sense. This includes Hougaard Levy processes such as the Poisson processes, Brownian motions with drift and the inverse Gaussian processes, and some new fractional Hougaard motions defined as moving averages of Hougaard Levy process. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes.

DNA sequences generated by BCH codes over GF(4)

The question raised by researchers in the field of mathematical biology regarding the existence of error-correcting codes in the structure of the DNA sequences is answered positively. It is shown, for the first time, that DNA sequences such as proteins, targeting sequences and internal sequences are identified as codewords of BCH codes over Galois fields.

A two-phase approach for detecting recombination in nucleotide sequences

Genetic recombination can produce heterogeneous phylogenetic histories within a set of homologous genes. Delineating recombination events is important in the study of molecular evolution, as inference of such events provides a clearer picture of the phylogenetic relationships among different gene sequences or genomes. Nevertheless, detecting recombination events can be a daunting task, as the performance of different recombination-detecting approaches can vary, depending on evolutionary events that take place after recombination. We recently evaluated the effects of post-recombination events on the prediction accuracy of recombination-detecting approaches using simulated nucleotide sequence data. The main conclusion, supported by other studies, is that one should not depend on a single method when searching for recombination events. In this paper, we introduce a two-phase strategy, applying three statistical measures to detect the occurrence of recombination events, and a Bayesian phylogenetic approach in delineating breakpoints of such events in nucleotide sequences. We evaluate the performance of these approaches using simulated data, and demonstrate the applicability of this strategy to empirical data. The two-phase strategy proves to be time-efficient when applied to large datasets, and yields high-confidence results.

Quantum noise in optical fibers. I. Stochastic equations

We analyze the quantum dynamics of radiation propagating in a single-mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum-noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This treatment allows quantum Langevin equations, which have a classical form except for additional quantum-noise terms, to be calculated. In practical calculations, it is more useful to transform to Wigner or 1P quasi-probability operator representations. These transformations result in stochastic equations that can be analyzed by use of perturbation theory or exact numerical techniques. The results have applications to fiber-optics communications, networking, and sensor technology.

Time-reversal test for stochastic quantum dynamics

The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultracold atomic Bose-Einstein condensates to condensed matter, biology, and even astrophysics. Here we demonstrate a conceptually simple method of determining the regime of validity of stochastic simulations of unitary quantum dynamics by employing a time-reversal test. We apply this test to a simulation of the evolution of a quantum anharmonic oscillator with up to 6.022×1023 (Avogadro's number) of particles. This system is realizable as a Bose-Einstein condensate in an optical lattice, for which the time-reversal procedure could be implemented experimentally.

Canonical Bose gas simulations with stochastic gauges

A technique to simulate the grand canonical ensembles of interacting Bose gases is presented. Results are generated for many temperatures by averaging over energy-weighted stochastic paths, each corresponding to a solution of coupled Gross-Pitaevskii equations with phase noise. The stochastic gauge method used relies on an off-diagonal coherent-state expansion, thus taking into account all quantum correlations. As an example, the second-order spatial correlation function and momentum distribution for an interacting 1D Bose gas are calculated.

Molecular phylogeny of Wolbachia endosymbionts in southeast asian mosquitoes (Diptera: Culicidae) based on wsp gene sequences

Wolbachia are maternally inherited intracellular bacteria that infect a wide range of arthropods and nematodes and are associated with various reproductive abnormalities in their hosts. Insect-associated Wolbachia form a monophyletic clade in the α-Proteobacteria and recently have been separated into two supergroups (A and B) and 19 groups. Our recent polymerase chain reaction (PCR) survey using wsp specific primers indicated that various strains of Wolbachia were present in mosquitoes collected from Southeast Asia. Here, we report the phylogenetic relationship of the Wolbachia strains found in these mosquitoes using wsp gene sequences. Our phylogenetic analysis revealed eight new Wolbachia strains, five in the A supergroup and three in the B supergroup. Most of the Wolbachia strains present in Southeast Asian mosquitoes belong to the established Mors, Con, and Pip groups.

wsp Gene sequences from the Wolbachia of filarial nematodes

Wolbachia endosymbiotic bacteria are widespread in arthropods and are also present in filarial nematodes. Almost all filarial species so far examined have been found to harbor these endosymbionts. The sequences of only three genes have been published for nematode Wolbachia (i.e., the genes coding for the proteins FtsZ and catalase and for 16S rRNA). Here we present the sequences of the genes coding for the Wolbachia surface protein (WSP) from the endosymbionts of eight species of filaria. Complete gene sequences were obtained from the endosymbionts of two different species, Dirofilaria immitis and Brugia malayi. These sequences allowed us to design general primers for amplification of the wsp gene from the Wolbachia of all filarial species examined. For these species, partial WSP sequences (about 600 base pairs) were obtained with these primers. Phylogenetic analysis groups these nematode wsp sequences into a coherent cluster. Within the nematode cluster, wsp-based Wolbachia phylogeny matches a previous phylogeny obtained with ftsZ gene sequences, with a good consistency of the phylogeny of hosts (nematodes) and symbionts (Wolbachia). In addition, different individuals of the same host species (Dirofilaria immitis and Wuchereria bancrofti) show identical wsp gene sequences.

Sampling phylogenetic tree space with the generalized Gibbs sampler

The generalized Gibbs sampler (GGS) is a recently developed Markov chain Monte Carlo (MCMC) technique that enables Gibbs-like sampling of state spaces that lack a convenient representation in terms of a fixed coordinate system. This paper describes a new sampler, called the tree sampler, which uses the GGS to sample from a state space consisting of phylogenetic trees. The tree sampler is useful for a wide range of phylogenetic applications, including Bayesian, maximum likelihood, and maximum parsimony methods. A fast new algorithm to search for a maximum parsimony phylogeny is presented, using the tree sampler in the context of simulated annealing. The mathematics underlying the algorithm is explained and its time complexity is analyzed. The method is tested on two large data sets consisting of 123 sequences and 500 sequences, respectively. The new algorithm is shown to compare very favorably in terms of speed and accuracy to the program DNAPARS from the PHYLIP package.

A two-phase strategy for detecting recombination in nucleotide sequences

Genetic recombination can produce heterogeneous phylogenetic histories within a set of homologous genes. Delineating recombination events is important in the study of molecular evolution, as inference of such events provides a clearer picture of the phylogenetic relationships among different gene sequences or genomes. Nevertheless, detecting recombination events can be a daunting task, as the performance of different recombination-detecting approaches can vary, depending on evolutionary events that take place after recombination. We previously evaluated the effects of post-recombination events on the prediction accuracy of recombination-detecting approaches using simulated nucleotide sequence data. The main conclusion, supported by other studies, is that one should not depend on a single method when searching for recombination events. In this paper, we introduce a two-phase strategy, applying three statistical measures to detect the occurrence of recombination events, and a Bayesian phylogenetic approach to delineate breakpoints of such events in nucleotide sequences. We evaluate the performance of these approaches using simulated data, and demonstrate the applicability of this strategy to empirical data. The two-phase strategy proves to be time-efficient when applied to large datasets, and yields high-confidence results.

Bellerophon: a program to detect chimeric sequences in multiple sequence alignments

Bellerophon is a program for detecting chimeric sequences in multiple sequence datasets by an adaption of partial treeing analysis. Bellerophon was specifically developed to detect 16S rRNA gene chimeras in PCR-clone libraries of environmental samples but can be applied to other nucleotide sequence alignments.

Cost functions and duality for stochastic technologies

Cost functions dual to stochastic production technologies are derived and their properties are discussed. These cost functions are shown to be consistent with expected-utility maximization without placing serious structural restrictions on the underlying technology.

PCR bias toward the wild-type k-ras and p53 sequences: Implications for PCR detection of mutations and cancer diagnosis

PCR-based cancer diagnosis requires detection of rare mutations in k-ras, p53 or other genes. The assumption has been that mutant and wild-type sequences amplify with near equal efficiency, so that they are eventually present in proportions representative of the starting material. Work factor IX suggests that this assumption is invalid for one case of near-sequence identity To test the generality of this phenomenon and its relevance to cancer diagnosis, primers distant from point mutations in p53 and k-ras were used to amplify, wild-type and mutant sequences from these genes. A substantial bias against PCR amplification of mutants was observed for two regions of the p53 gene and one region of k-ras. For kras and p53, bias was observed when the wild-type and mutant sequences were amplified separately or when mixed in equal proportions before PCR. Bias was present with proofreading and non-proofreading polymerases. Mutant and wild-type segments of the factor V cystic fibrosis transmembrane conductance regulator and prothrombin genes were amplified and did not exhibit PCR bias. Therefore, the assumption of equal PCR efficiency for point mutant and wild-type sequences is invalid in several systems. Quantitative or diagnostic PCR will require validation for each locus, and enrichment strategies may be needed to optimize detection of mutants.